At (REF ) the marginals \(F_{Y_j}\)  are assumed independent
of the covariates, while the copula is not.
In contrast, the copula can be assumed to be independent of the covariates,
while the marginals are not; for examples, see [1]}, [2]} and [3]}. The first approach defines
a copula process for a univariate response,
whereas the latter approach defines
a multivariate regression model for multiple response variables.
